Question: In this diagram, both polygons are regular. What is the value, in degrees, of the sum of the measures of angles $ABC$ and $ABD$? [asy] draw(10dir(0)--10dir(60)--10dir(120)--10dir(180)--10dir(240)--10dir(300)--10dir(360)--cycle,linewidth(2)); draw(10dir(240)--10dir(300)--10dir(300)+(0,-10)--10dir(240)+(0,-10)--10dir(240)--cycle,linewidth(2)); draw(10dir(300)+(-1,0)..9dir(300)..10dir(300)+dir(60),linewidth(2)); draw(10dir(300)+(-1.5,0)..10dir(300)+1.5dir(-135)..10dir(300)+(0,-1.5),linewidth(2)); label("A",10dir(240),W); label("B",10dir(300),E); label("C",10dir(0),E); label("D",10dir(300)+(0,-10),E); draw(10dir(300)+2dir(-135)--10dir(300)+dir(-135),linewidth(2)); [/asy]
Answer: The interior angle of a square is 90, and the interior angle of a hexagon is 120, making for a sum of $\boxed{210}$. If you don't have the interior angles memorized, you can calculate them using the following formula: $180\left(\frac{n-2}{n}\right),$ where $n$ is the number of sides in the polygon.